MCAT Thermodynamics Practice Problems

Aug 20, 2024

MCAT General Physics: Thermodynamics Practice Lecture

Overview

This lecture focuses on practicing thermodynamics problems for the MCAT General Physics section. Key concepts include temperature conversions, heat transfer processes, thermal expansion, and calorimetry.

Temperature Conversions

  • Problem: Calculate the increase in degrees Fahrenheit for an object initially at 300K, increasing 1°C every minute for 10 minutes.
  • Concepts:
    • Kelvin and Celsius are equivalent in terms of change.
    • 10°C change equals 10K change.
    • Conversion from Celsius to Fahrenheit: multiply by 1.8.
    • Answer: 18°F increase.

Heat Transfer Processes

  • Problem 1: Identify the heat transfer process for three scenarios.
    • Radiation: Heat transfer from Sun to Earth.
    • Conduction: Metal spoon in hot soup.
    • Convection: Rising smoke from a fire.
    • Answer: Radiation, Conduction, Convection.

Thermal Expansion

  • Problem 2: Determine if a heated steel rod touches the ground.
    • Use the thermal expansion equation: ∆L = αL∆T.
    • Given: α (thermal expansion coefficient), initial length, and temperature change.
    • Calculation: Rod increases by 1.76 cm, does not touch the ground.
    • Answer: No, rod does not touch ground.

Heating and Final Temperature

  • Problem 3: Final temperature of a silver pendant heated for 10 minutes at 100 watts.
    • Convert power to energy: Power (W) × Time (s).
    • Use heat equation: Q = mc∆T.
    • Solve for final temperature.
    • Answer: Final temperature is 72°C.

Heat Required to Melt Gold

  • Problem 4: Calculate heat required to melt gold earrings.
    • Steps:
      1. Heat to raise temperature to melting point.
      2. Heat to melt (latent heat of fusion).
    • Use MCAT equation and latent heat.
    • Answer: Total heat required is approximately 92 kJ.

Work Done by Gas

  • Problem 5: Calculate total work done by gas in a cycle.
    • Area of triangle formed by paths a, b, c: ½(base × height).
    • Clockwise cycle indicates positive work.
    • Answer: 7.5 Joules.

Adiabatic Processes

  • Problem 6: Internal energy change during adiabatic compression.
    • Definition: No heat exchange (Q=0), U = -W.
    • Compression implies positive work done on gas.
    • Answer: Internal energy increases.

Entropy

  • Problem 7: Entropy behavior in a system.
    • Entropy can decrease if the surrounding entropy increases more.
    • Second Law of Thermodynamics applied.
    • Answer: Decrease when surroundings increase more.

Calorimetry

  • Problem 8: Effect of improper calorimeter setup.
    • Goal: Isolate system (no heat or matter exchange).
    • Failure results in open system with potential heat/matter exchange.
    • Answer: Created an open system.

Melting Energy Calculation

  • Problem 9: Energy required to melt a substance at specific heat and melting point.
    • Calculate energy to raise temperature to melting point, then energy to melt.
    • Answer: 1 Joule to reach melting point, more needed to melt.

These problems cover essential thermodynamic principles necessary for the MCAT, focusing on practical applications and problem-solving skills.